Combining hierarchy and energy for drawing directed graphs

Liran Carmel; David Harel; Yehuda Koren

doi:10.1109/TVCG.2004.1260757

Combining hierarchy and energy for drawing directed graphs

Liran Carmel^*, David Harel, Yehuda Koren

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

We present an algorithm for drawing directed graphs which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

Original language	American English
Pages (from-to)	46-57
Number of pages	12
Journal	IEEE Transactions on Visualization and Computer Graphics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1109/TVCG.2004.1260757
State	Published - Jan 2004
Externally published	Yes

Keywords

Directed graph drawing
Fiedler vector
Force directed layout
Hierarchy energy
Minimum linear arrangement

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10.1109/TVCG.2004.1260757

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AB - We present an algorithm for drawing directed graphs which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

KW - Directed graph drawing

KW - Fiedler vector

KW - Force directed layout

KW - Hierarchy energy

KW - Minimum linear arrangement

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Combining hierarchy and energy for drawing directed graphs

Abstract

Keywords

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